Compass Surveying Calculator
🔄 Convert WCB to RB
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🧠Convert RB to WCB
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Complete Guide to Compass Surveying Bearings
In civil engineering, the direction of a survey line is defined by its horizontal angle relative to a fixed reference line (North). There are two main systems: Whole Circle Bearing (WCB) and Reduced Bearing (RB).
1. Whole Circle Bearing (WCB)
Measured clockwise from Magnetic North. The value ranges from \(0^\circ\) to \(360^\circ\).
Instrument: Prismatic Compass.
2. Reduced Bearing (RB) or Quadrantal Bearing
Measured from North or South towards East or West. The angle is always between \(0^\circ\) and \(90^\circ\).
Instrument: Surveyor's Compass.
Conversion Formulas Table
To convert, identify the Quadrant the line falls into:
| Quadrant | WCB Range | RB Formula | WCB Formula |
|---|---|---|---|
| I (N-E) | \(0^\circ - 90^\circ\) | \(\text{RB} = \text{WCB}\) | \(\text{WCB} = \text{RB}\) |
| II (S-E) | \(90^\circ - 180^\circ\) | \(\text{RB} = 180^\circ - \text{WCB}\) | \(\text{WCB} = 180^\circ - \text{RB}\) |
| III (S-W) | \(180^\circ - 270^\circ\) | \(\text{RB} = \text{WCB} - 180^\circ\) | \(\text{WCB} = 180^\circ + \text{RB}\) |
| IV (N-W) | \(270^\circ - 360^\circ\) | \(\text{RB} = 360^\circ - \text{WCB}\) | \(\text{WCB} = 360^\circ - \text{RB}\) |
Solved Numerical Examples
Example 1: Convert WCB \(145^\circ 30'\) to Reduced Bearing (RB).
1. Check Quadrant: \(145^\circ\) is between \(90^\circ\) and \(180^\circ\) (II Quadrant, S-E).
2. Formula: \(\text{RB} = 180^\circ - \text{WCB}\)
3. Calculation: \(179^\circ 60' - 145^\circ 30' = 34^\circ 30'\)
4. Result: \(S \ 34^\circ 30' \ E\)
1. Check Quadrant: \(145^\circ\) is between \(90^\circ\) and \(180^\circ\) (II Quadrant, S-E).
2. Formula: \(\text{RB} = 180^\circ - \text{WCB}\)
3. Calculation: \(179^\circ 60' - 145^\circ 30' = 34^\circ 30'\)
4. Result: \(S \ 34^\circ 30' \ E\)
Example 2: Convert RB \(N \ 25^\circ \ W\) to WCB.
1. Check Quadrant: \(N...W\) is the IV Quadrant.
2. Formula: \(\text{WCB} = 360^\circ - \text{RB}\)
3. Calculation: \(360^\circ - 25^\circ\)
4. Result: \(335^\circ\)
1. Check Quadrant: \(N...W\) is the IV Quadrant.
2. Formula: \(\text{WCB} = 360^\circ - \text{RB}\)
3. Calculation: \(360^\circ - 25^\circ\)
4. Result: \(335^\circ\)
Frequently Asked Questions (FAQ)
Q: Which compass uses WCB?
The Prismatic Compass measures Whole Circle Bearings (0-360°).
Q: Which compass uses RB?
The Surveyor's Compass measures Reduced Bearings (0-90°).